Calculate the ratio of rms speeds of oxygen gas molecules to that of hydrogen gas molecules kept at the same temperature.

Question

Calculate the ratio of rms speeds of oxygen gas molecules to that of hydrogen gas molecules kept at the same temperature. (A)  1: 4  (B)  1: 8  (C)  1: 2  (D)  1: 6

Tardigrade Admin · Accepted Answer

Root mean square velocity Vrms propto(1/√M) so ((Vrms)O2/(Vrms)H2)=√(MH2/MO2) =√(2/32)=(1/4)

Q. Calculate the ratio of $r m s$ speeds of oxygen gas molecules to that of hydrogen gas molecules kept at the same temperature.

$1 : 4$

$1 : 8$

$1 : 2$

$1 : 6$

Root mean square velocity
$V_{r m s} \propto \frac{1}{M}$
so $\frac{( V _{r m s} ) O _{2}}{( V _{r m s} ) H _{2}} = \frac{M _{H_{2}}}{M _{O_{2}}}$
$= \frac{2}{32} = \frac{1}{4}$

Q. Calculate the ratio of rms speeds of oxygen gas molecules to that of hydrogen gas molecules kept at the same temperature.

1:4

1:8

1:2

1:6